Parity NIM

Parity NIM consists of a pile containing an odd number of objects from which players take turns removing one or more objects, with at most \(k\) objects removed by each player during his or her turn. The player who has removed an odd number of objects at the end of the game wins.  If \(n\) is the number of objects in the initial pile, a specific solution for the pair \((n,k)\) can be found.   However, no general solution is known.